Question

Find the quotient when the polynomial $2x^3+2x^2+2$ is divided by $x-3$ using synthetic division method.

• A. $7x^2+8x+24$
• B. $2x^2+8x+26$
• C. $2x^2+8x+24$
• D. $2x^2+3x+24$

Answer 1

The correct option is C $2x^2+8x+24$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Index form of the dividend polynomial is :

$2x^3+2x^2+2=2x^3+2x^2+0x+2$

Coefficient form of the dividend polynomial is :

(2,2,0,2)

Divisor polynomial =x-3

Steps:
1. Draw the horizontal and vertical lines as below :



2. Divisor is x-3. Take opposite number of -3 which is 3.Write 3 to the left of the vertical line. Write the coefficient form of the dividend polynomial in the first row and write the first coefficient as it is in the third row

$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 2& 2& 0& 2\\ 3& \downarrow & & & \\ & 2& & & \end{array}$

3. The product of 2 in the third row
with divisor 3 is 6. Write this 6 in the second row below the coefficient 2. Addition of 2 and 6 which is 8, is to be written in the third row.

Similarly by multiplying and adding, we have

$\begin{array}{ccccc}& x^3& x^2& x^1& x^0\\ & 2& 2& 0& 2\\ 3& \downarrow & 6& 24& 72\\ & 2& 8& 24& |-74\end{array}$

The last addition is the remainder, which is ' 74 '.

The coefficient form of the quotient is (2, 8, 24).

So, quotient is $2x^2+8x+24$, remainder is '74'.